Temperature compensation for mems devices

ABSTRACT

A microelectromechanical system (MEMS) device includes a temperature compensating structure including a first beam suspended from a substrate and a second beam suspended from the substrate. The first beam is formed from a first material having a first Young&#39;s modulus temperature coefficient. The second beam is formed from a second material having a second Young&#39;s modulus temperature coefficient. The body may include a routing spring suspended from the substrate. The routing spring may be coupled to the first beam and the second beam. The routing spring may be formed from the second material. The first beam and the second beam may have lower spring compliance than the routing spring. The MEMS device may be a resonator and the temperature compensating structure may have dimensions and a location such that the temperature compensation structure modifies a temperature coefficient of frequency of the resonator independent of a mode shape of the resonator.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims benefit under 35 U.S.C. §119 of provisionalapplication No. 61/831,324, entitled “Monolithic Body MEMS Devices,”filed Jun. 5, 2013, which application is hereby incorporated byreference.

BACKGROUND

1. Field of the Invention

The invention is related to microelectromechanical systems (MEMS).

2. Description of the Related Art

In general, microelectromechanical systems (MEMS) are very smallmechanical devices. Typical MEMS devices include sensors and actuators,which may be used in various applications, e.g., resonators (e.g.,oscillators), temperature sensors, pressure sensors, or inertial sensors(e.g., accelerometers or angular rate sensors). The mechanical device istypically capable of some form of mechanical motion and is formed at themicro-scale using fabrication techniques similar to those utilized inthe microelectronic industry, such as using lithography, deposition, andetching processes.

In general, a MEMS transducer converts energy between different forms,e.g., electrostatic and mechanical forms. MEMS transducers may be usedas both sensors that convert motion into electrical energy(accelerometers, pressure sensors, etc.) and actuators that convertelectrical signals to motion (comb drive, micromirror devices,resonators). MEMS devices using capacitive transducers are easy tomanufacture and result in low noise and low power consumption sensorsand/or actuators.

Capacitive sensing is based on detecting a change in capacitance of acapacitor. If a known voltage is applied across the capacitor (e.g.,fixed DC potential differences applied across the capacitors a the MEMSdevice), changes in current due to capacitive variations will appear inresponse to motion of one plate of the capacitor relative to anotherplate of the capacitor. Similarly, capacitive actuation is based onvariation in electrostatic forces between the two plates of a MEMScapacitive transducer. For example, a DC operating point can beestablished by applying a DC bias voltage across the capacitor and an ACvoltage causing changes in force on a plate of the capacitor.Transduction of a MEMS device is based on the voltage across thetransduction gap generating an electrostatic force, or inversely,transduction based on the gap variation due to displacement generating acharge variation at the output of the transducer. The transduction gapmay vary as a function of environmental factors (e.g., temperature,strain, and aging), thereby changing the capacitance with respect totime. These same environmental factors can also affect the springconstant (i.e., spring stiffness) associated with a MEMS device, whichis typically modeled as a mass-spring-damper system. In general, achange in the electrode capacitance affects the equivalent springstiffness through electrostatic pulling, which affects the resonantfrequency of the MEMS device. MEMS devices targeting applicationsrequiring high-precision (e.g., resonators having resonant frequencyspecifications required to be within +/−10 parts-per-million (ppm)) maynot achieve the target specification due to effects of environmentalfactors on the resonant frequency.

A MEMS device may be configured as a resonator that is used in timingdevices. The resonator may have a variety of physical shapes, e.g.,beams and plates. The MEMS device may have a portion suspended from thesubstrate (e.g., a suspended mass, body, or resonator) attached to thesubstrate by an anchor. An exemplary suspended mass may be a featuresuch as, but not limited to, a beam, a plate, a cantilever arm, or atuning fork. In a specific embodiment, a MEMS device includes aresonating feature (e.g., suspended mass) flanked by one or more driveelectrodes and one or more sense electrodes.

Referring to FIG. 1, a conventional MEMS device (e.g., MEMS device 100)includes resonator 105 coupled to substrate 102 via anchor 104. Duringoperation, electrode 110 electrostatically drives resonator 105 todynamically deflect, which increases a capacitance between resonator 105and electrode 110 when a voltage differential exists between resonator105 and electrode 110 by decreasing the gap between resonator 105 andelectrode 110. Since electrode 110 and resonator 105 are the same heightand thickness and are in the same plane, resonator 105, when driven,deforms laterally, i.e., parallel to the plane of the substrate, acrossa distance between electrode 110 and a second electrode 111. Electrode110 is substantially parallel to substrate 102. Electrode 111 detectsthe resonant frequency of resonator 105 as the capacitance variesbetween resonator 105 and electrode 111 in response to the deflectiondriven by electrode 110. MEMS device 100 is commonly referred to as an“in-plane” or “lateral” mode resonator because resonator 105 is drivento resonate in a mode where the resonator 105 moves laterally (indirection 109) and remains aligned vertically with electrode 110.

Referring to FIG. 2, in an exemplary MEMS application, MEMS device 100is coupled to amplifier 210 in an oscillator configuration. Senseelectrode 202 provides a signal based on energy transfer from avibrating resonator of MEMS device 100, thereby converting mechanicalenergy into an electrical signal. In general, bias signals introduced atvarious points of the circuit determine an operating point of thecircuit and may be predetermined, fixed DC voltages or currents added toAC signals. The resonator of MEMS device 100 receives a DC bias voltage,V_(RES), which is generated by a precision voltage reference or voltageregulator of bias generator 206. However, in other embodiments, biassignals may be introduced at the electrodes and/or other nodes of theoscillator circuit. A large feedback resistor (R_(F)) biases amplifier210 in a linear region of operation, thereby causing amplifier 210 tooperate as a high-gain inverting amplifier. The MEMS oscillator sustainsvibrations of MEMS device 100 by feeding back the output of amplifier210 to a drive electrode of MEMS device 100. Amplifier 210 receives asmall-signal voltage from sense electrode 202 and generates a voltage ondrive electrode 204 that causes the resonator of MEMS device 100 tocontinue to vibrate. MEMS device 100 in combination with capacitances C₁and C₂ form a pi-network band-pass filter that provides 180 degrees ofphase shift and a voltage gain from drive electrode 204 to senseelectrode 202 at approximately the resonant frequency of MEMS device100.

For some MEMS applications (e.g., a low-power clock source), alow-power, high-Q (i.e., quality factor), stable, and accurateoscillator may be required. However, the power, accuracy, and stabilityspecifications may be difficult to achieve using the conventional MEMSdevice of FIG. 1. Accordingly, improved MEMS devices, e.g., MEMS devicesthat reduce or eliminate factors that affect accuracy and reliability ofthe output frequency of the MEMS device, are desired.

SUMMARY

In at least one embodiment of the invention, an apparatus includes amicroelectromechanical system (MEMS) device including a first electrodeand a second electrode. The MEMS device includes a body suspended from asubstrate. The body and the first electrode form a first electrostatictransducer. The body and the second electrode form a secondelectrostatic transducer. The body comprises a temperature compensatingstructure. The temperature compensating structure includes a first beamsuspended from the substrate. The first beam is formed from a firstmaterial having a first Young's modulus temperature coefficient. Thetemperature compensating structure includes a second beam suspended fromthe substrate. The second beam is formed from a second material having asecond Young's modulus temperature coefficient. The second material mayhave a higher electrical conductivity than the first material. The firstbeam and the second beam may be mechanically coupled in series. The bodymay include a routing spring suspended from the substrate. The routingspring may be coupled to the first beam and the second beam. The routingspring may be formed from the second material. The first beam and thesecond beam may have lower spring compliance than the routing spring.The MEMS device may be a resonator and the temperature compensatingstructure has dimensions and a location such that the temperaturecompensation structure modifies a temperature coefficient of frequencyof the resonator independent of a mode shape of the resonator.

In at least one embodiment of the invention, a method of manufacturingan apparatus includes forming a MEMS. The MEMS device includes a firstelectrode and a second electrode. The MEMS device includes a bodysuspended from a substrate. The body and the first electrode form afirst electrostatic transducer. The body and the second electrode form asecond electrostatic transducer. The body includes a temperaturecompensating structure. The temperature compensating structure includesa first beam suspended from the substrate. The first beam is formed froma first material having a first Young's modulus temperature coefficient.The temperature compensating structure includes a second beam suspendedfrom the substrate. The second beam is formed from a second materialhaving a second Young's modulus temperature coefficient. The secondmaterial may have a higher electrical conductivity than the firstmaterial. The first beam and the second beam may be mechanically coupledin series. The MEMS device may include a routing spring suspended fromthe substrate. The routing spring may be coupled to the first beam andthe second beam. The routing spring may be formed from the secondmaterial. The routing spring may have a serpentine structure. The firstbeam and the second beam may have lower spring compliances than therouting spring.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may be better understood, and its numerousobjects, features, and advantages made apparent to those skilled in theart by referencing the accompanying drawings.

FIG. 1 illustrates a conventional MEMS device including an in-planeresonator.

FIG. 2 illustrates a circuit diagram of a MEMS device configured as anoscillator.

FIG. 3 illustrates an exemplary cross-sectional view of a MEMS structureprior to a release of a structural layer to form suspended portionsconsistent with at least one embodiment of the invention.

FIG. 4A illustrates a diagram modeling a typical MEMS transducer.

FIG. 4B illustrates a diagram modeling a MEMS transducer having asuspended electrode and a suspended resonator consistent with at leastone embodiment of the invention.

FIG. 4C illustrates a diagram modeling a MEMS transducer having asuspended electrode and a suspended resonator in a coupled electrodeconfiguration consistent with at least one embodiment of the invention.

FIG. 5 illustrates a plan view of a MEMS transducer having a suspendedelectrode and resonator in a coupled electrode configuration consistentwith at least one embodiment of the invention.

FIGS. 6A-6D illustrates various features of the MEMS transducer of FIG.5 having a suspended electrode and resonator in a coupled electrodeconfiguration consistent with at least one embodiment of the invention.

FIG. 6E illustrates static deflection after stress relief of the MEMStransducer of FIG. 5 having a suspended electrode and resonator in acoupled electrode configuration consistent with at least one embodimentof the invention.

FIG. 7A illustrates dynamic mode shape of a high frequency MEMStransducer without suspended electrodes.

FIG. 7B illustrates a plan view of the high frequency MEMS transducerwithout suspended electrodes of FIG. 7A.

FIGS. 8A and 8B illustrate a plan view of a high frequency MEMStransducer with suspended electrodes consistent with at least oneembodiment of the invention.

FIG. 9 illustrates a coupled electrode device consistent with at leastone embodiment of the invention.

FIGS. 10A and 10B illustrate a suspended resistor device consistent withat least one embodiment of the invention.

FIG. 10C illustrates a suspended resistor device and a MEMS transducerhaving lateral electrodes consistent with at least one embodiment of theinvention.

The use of the same reference symbols in different drawings indicatessimilar or identical items.

DETAILED DESCRIPTION

Referring back to FIG. 1, MEMS device 100 may be modeled as aspring-mass system having a resonant frequency,

${f_{0} = {\frac{1}{2\pi}\sqrt{\frac{k}{m}}}},$

where k is a constant indicative of the spring stiffness, m is mass ofthe resonator, and f₀ is the resonant frequency. In general, the qualityfactor, Q, characterizes a resonator's bandwidth relative to its centerfrequency. The quality factor may be represented as Q=2πf_(o)m/γ, whereγ is damping coefficient (e.g., due to fluid in a cavity surrounding themass). A higher Q indicates a lower rate of energy loss relative to thestored energy of the resonator, i.e., oscillations die out more slowly.An oscillator with a higher Q resonates with higher amplitude but for asmaller range of frequencies around that frequency over smallerbandwidth. To achieve a high-precision, low-power resonator, a high massmay be desired so that the device can have a high stiffness. Increasingmass m increases the quality factor of the resonator if the otherrelevant parameters for Q are held constant. To maintain a particularresonant frequency, an increase in m requires a corresponding increasein k. Other design goals for particular MEMS applications may includelow-frequency operation (e.g., f₀<1 MHz) and insensitivity to shocks tothe housing of the MEMS oscillator. A high stiffness reduces sensitivityto resonator voltage and reduces nonlinearities in operation. However,device characteristics influencing transducer linearity and mechanicalstiffness can be altered by environmental changes, which may affect theinitial accuracy of frequency and stability of frequency in response toaging and temperature variation.

The typical MEMS device of FIG. 1 is made of a movable free standingbody, and one or more electrodes, all of which may be at differentelectrical potentials. A combination of an electrode and a body forms anelectro-mechanical transducer. The electrostatic transducer formed by anelectrode and mass is subjected to environmental factors liketemperature variation and mechanical strain which can influence itsproperties and in turn affects critical performance of the overall MEMSdevice, like initial accuracy. The typical MEMS device uses two separatebodies for an electrode and a movable mass. In general, these bodies areanchored separately from each other and as a result, the transducer gapformed between the two (having a width d) is susceptible to strainresulting from residual stress from the structural layer, coefficient ofthermal expansion mismatch between a structural layer (e.g., SiGe) andthe substrate (e.g., Si), and/or stress from the package, which willgenerally vary with temperature, and possibly with time (e.g., stressrelaxation).

Such variation in transducer properties impacts electromechanicalbehavior and may manifest itself in frequency variation due to strain inresonator applications or acceleration offset and sensitivity ininertial sensor applications and may limit performance or tolerances ofa MEMS system. For example, in a typical MEMS resonator application, aMEMS oscillator may be calibrated to meet a +/−10, 20, or 50parts-per-million (ppm) at room temperature and over temperature. If thetransducer is sensitive to strain, package strain variations due tosolder reflow or temperature variations will modify the electrostaticforce of the transducer, which affects the resonant frequency of thedevice. Frequency variation due to strain variation may result in theMEMS resonator failing to meet a target specification.

Ideally, to reduce the effects of strain on a MEMS device, electrodeanchors and resonator anchors can be placed as close to each other aspractical. As referred to herein, an anchor is a structure thatmechanically couples (e.g., anchors, fixes, fastens, joins, connects, orattaches) a portion of a first structure to a portion of a secondstructure. Portions of the first and second structures that aremechanically coupled have restricted motion. In conventional MEMSdevices, locating the electrode anchors and resonator anchors in thesame location on a substrate is not typically feasible. Therefore, theelectrode and resonator anchors of the MEMS device are located in closeproximity (e.g., as close as allowable by design constraints (e.g.,design rules) for the target manufacturing process) to reducesensitivity of MEMS device to the effects of strain on the MEMS device.Transduction of the MEMS device is often based on the voltage differenceacross the transduction gap (i.e., the voltage difference between themass and the electrode, V_(ME)). For example, the transduction gap of anexemplary MEMS device is defined by the distances between the capacitivefingers of the resonator and corresponding capacitive fingers of anelectrode, which may be equal. Those distances may vary as a function ofstrain, causing a change to the capacitive transduction of MEMS deviceand thus causing a change to the resonant frequency.

A technique decouples transducers of the MEMS device from sources ofstrain by forming a MEMS structure with suspended electrodes that aremechanically anchored in a manner that reduces or eliminates thetransfer strain from the substrate into the structure (e.g., by usingone or more center anchor structure), or transfers strain to bothelectrodes and body in such a way that the transducer remains invariant.The technique includes using an electrical insulator material (e.g.,SiO₂) embedded in a conductive structural material (e.g., SiGe) both formechanical coupling and electrical isolation. As referred to herein, astructural layer is a layer of a particular material that is laterpatterned and at least partially released to form at least a portionthat is free to mechanically move or be deflected in at least onedirection with respect to a surface of a substrate. As referred toherein, a release of a structure or a portion of a structural layerfrees that structure or portion of the structural layer to have aportion that is free to mechanically move or be deflected in at leastone directional plane with respect to the substrate. A release layer isa layer of material that, when removed, releases at least a portion ofthe structure or structural layer. The release typically occurs towardsthe end of manufacture to maintain integrity of the released structures.

The embedded electrical insulator material may also be used fortemperature compensation of MEMS devices, which is described in U.S.Pat. No. 7,639,104, filed Mar. 9, 2007 (issued Dec. 29, 2009), entitled“Method for Temperature Compensation in MEMS Resonators with IsolatedRegions of Distinct Material,” naming Emmanuel P. Quevy et al., asinventors, which application is incorporated herein by reference. Theembedded electrical insulator material may be used to electricallyisolate specific areas of the structural layer. The embedded electricalinsulator may be used to route different signals through the structurallayer while keeping a continuous (i.e., monolithic) mechanical body.Although the technique is described using silicon dioxide, otherelectrically insulating materials may be used. Techniques for formingthe electrically insulating material structures (e.g., embedded silicondioxide slits) are described in U.S. Pat. No. 7,639,104 and described inU.S. Pat. No. 7,514,760, entitled “IC-Compatible MEMS Structure” namingEmmanuel P. Quevy as inventor, filed Mar. 9, 2007, issued Apr. 7, 2009,which application is incorporated herein by reference.

One or more embedded electrical insulator slits may be used to routesignals and perform electrical, thermal, and mechanical functionssimultaneously. In at least one embodiment of a MEMS device, embeddedinsulator material is used to form a monolithic MEMS device, whichincludes a self-referenced transducer gap, i.e., the electrode andmovable body are mechanically coupled to move together, thereby reducingthe impact of environmental strain. In at least one embodiment of a MEMSdevice formed using embedded insulator material, an electrode is part ofthe movable body and contributes to the mode shape. In at least oneembodiment of a MEMS device formed using embedded insulator material,the electrode is a movable body and contributes to the relativedisplacement of body versus electrode. As a result, those MEMS devicesmay have more compact designs with higher performance (e.g., highersignal-to-noise ratio versus area). In addition, the embedded electricalinsulator material slit technique allows the routing of separate signalswithin the same structural layer.

Referring to FIG. 3, an exemplary MEMS device that achieves high-Qoperation is manufactured using techniques that form body and electrodestructures that are suspended from a substrate. Manufacturing techniquesthat may be used to produce MEMS devices are described in U.S. Pat. No.7,514,760, filed Mar. 9, 2007, entitled “IC-Compatible MEMS Structure,”naming Emmanuel P. Quevy as inventor; U.S. patent application Ser. No.13/075,800, filed Mar. 30, 2011, entitled “Technique for Forming a MEMSDevice,” naming Emmanuel P. Quevy et al., as inventors; and U.S. patentapplication Ser. No. 13/075,806, filed Mar. 30, 2011, entitled“Technique for Forming a MEMS Device Using Island Structures,” namingEmmanuel P. Quevy et al., as inventors, which applications areincorporated herein by reference. For example, structural layer 302includes structural portions 304 and 306 that are electrically isolated,but mechanically coupled to each other using embedded isolation oxide308. Upon release of the structural material, structural portions 304and 306 are suspended from substrate 312. Structural portions areelectrically coupled to electrical domains using electrical contactstructures 314, 316, and 318. Signals may be routed using embeddedinsulator portions, while maintaining a continuous (i.e., monolithic)mechanical body as discussed further below.

Referring to FIG. 4A, a typical electrostatic transducer includes amovable mass 402 anchored to a substrate 420 and a movable electrodeanchored to the substrate 420. The electrostatic transducer has atransducer gap, d, a resonator-electrode voltage V_(re), aresonator-electrode capacitance C_(re), and has an efficiency of

${{{\Gamma = {V_{re}\frac{\partial C_{re}}{\partial x}\frac{\partial x}{\partial t}}},{{{where}\mspace{14mu} C_{re}} = {\frac{ɛ_{0}A}{d_{0} - x}\mspace{14mu} {and}\mspace{14mu} \frac{\partial C_{re}}{\partial x}}}}}_{x = 0} = {\frac{C_{re}(0)}{d_{0}}.}$

Frequency variation due to strain, etc., results in a resonant frequencyof f_(osc)=f_(mech)*√{square root over (1−β(d)V²)}, where straindependence (from residual stress and thermal stress) of frequencyaccuracy is

${{\delta ɛ}\left( {\sigma,T} \right)} = {\frac{ɛ}{d_{0}}.}$

The resulting frequency shift due to strain is:

$\frac{\Delta \; f}{f}{{\left. \left( {\delta \; ɛ} \right) \right.\sim\frac{1}{2}} \cdot {\frac{3\delta \; {ɛ \cdot {\beta \left( d_{0} \right)} \cdot V^{2}}}{1 - {{\beta \left( d_{0} \right)} \cdot V^{2}}}.}}$

Frequency control applications may attempt to reduce or eliminate thisfrequency shift by reducing or eliminating the frequency variation dueto strain and/or reducing or eliminating the strain communicated to thedevice transducer.

Referring to FIG. 4B, a suspended electrode (represented by plate 422coupled to a spring-damper system) and suspended body (represented bymass 424 coupled to a spring-damper system) configuration results in atransducer gap, d, that only depends on the topological mismatch betweenelectrode and body. The suspended electrode and body are electricallyisolated and mechanically coupled by electrically insulating material406 in mechanical suspension 408. The topological mismatch (e.g.,electrode and body mismatch due to stress) can be tailored or nulled outby design. Referring to FIG. 4C, in a coupled electrode resonant mode,each electrode is a resonant body and is mechanically coupled to theother electrode to achieve the target resonant mode shape. Theelectrodes are electrically isolated and mechanically coupled usingelectrically insulating material 410 in mechanical suspension 412.

FIG. 5 illustrates an exemplary embodiment of a low frequency resonatorhaving a suspended electrode and a suspended body (i.e., resonator ormass). Low frequency resonators are typically sensitive to frequencyshift due to strain because of their low stiffness. MEMS device 500includes a comb drive transducer, which is used in some applications forimproved linearity of capacitance as a function of displacement. Theelectrodes and resonator of MEMS device 500 include electricallyconductive comb structures, which include rows of electrode teeth thatinterlock, but do not touch, rows of body teeth. The body and electrodesmove longitudinally, in-plane. However, techniques described herein maybe adapted to embodiments of a MEMS device including parallel platetransducers and/or those in which the body and/or electrodes moveout-of-plane.

Still referring to FIG. 5, in MEMS device 500, suspension beams 512 and513 include signal routing that extends through center anchor 504 ofbody 502. Body 502 includes folded beam springs. Alternately, thesuspension beams made from different materials may be configured inparallel physically and mechanically, instead of the folded spring shownhaving suspension beams mechanically in series but physically parallel.In the alternate case, the signal routing portion is not needed.Location of anchor 504 in the center of the body reduces transfer ofmechanical stress to the vibrating structure. Anchor 504 is a monolithicstructure, including multiple mechanically coupled portions. However,anchor 504 is partitioned into multiple electrically isolated portions(e.g., portions including contacts 503, 505, 507, 509, and 511 toseparate electrical domains for a first electrode, a body, and a secondelectrode, described further below with reference to FIGS. 6A-6C).Referring back to FIG. 5, the relatively large mass per area of the bodyof MEMS device 500 increases the stiffness of the folded beam for agiven frequency, thereby reducing frequency variation due to strain ascompared to MEMS devices having less mass for the same target frequency.Body 502 of MEMS device 500 also includes embedded oxide slits 522 tomatch the static deflection of the suspension beam in order to alignindividual transducer faces once residual stress is relieved in theentire structure, as discussed further below. Note that in FIG. 5,electrically insulating material is shaded with hatching andelectrically conductive material is shaded with dots. The unshaded gaps,e.g., between the electrode teeth and body teeth, may contain air orother fluid.

Referring to FIGS. 5 and 6A-6E, various features of MEMS device 500 areillustrated. Referring to FIG. 6A, electrically conductive portions ofbody 502 are coupled to a first electrical domain via contact 503 ofanchor 504. Body 502 is suspended from the substrate by beams 512 and513 extending between center anchor 504 and ends of body 502. Thehatched regions of MEMS device 500 in FIG. 6A indicate those portions ofMEMS device 500 that are coupled to the first electrical domain, otherportions of MEMS device 500 (electrically conductive and electricallyinsulating) are indicated with dots, and unshaded gaps, e.g., betweenthe electrode teeth and body teeth, may contain air or other fluid.Referring back to FIG. 5, conductive portions of beams 512 and 513 aredelineated as part of the first electrical domain by electricallyinsulating material embedded in beams 512 and 513 (indicated by hatchingin FIG. 5). Other portions of beams 512 and 513 are electricallyisolated from the first electrical domain by that embedded electricallyinsulating material. Body 502 includes conductive finger structures thatare interdigitated with conductive finger structures of electrodes toform comb drive transducers.

Referring to FIG. 6B, a first electrode of MEMS device 500 is coupled toa second electrical domain via contacts 505 and 507 of anchor 504.Portions of the first electrode are suspended from the substrate by beam512 extending between the center anchor structure and ends of the body.The hatched regions of MEMS device 500 in FIG. 6B indicate thoseportions of MEMS device 500 that are coupled to the second electricaldomain, other portions of MEMS device 500 (electrically conductive andelectrically insulating) are indicated with dots, and unshaded gaps,e.g., between the electrode teeth and body teeth, may contain air orother fluid. Referring back to FIG. 5, suspension beam 512 includesconductive portions that are defined as part of the second electricaldomain by electrical isolation material 515 embedded in beam 512.However, other portions of beam 512 are electrically isolated from thesecond electrical domain by that embedded electrical isolation material.The first electrode includes conductive finger structures that areinterdigitated with conductive finger structures of body 502 to formcomb drive transducers.

Referring to FIG. 6C, a second electrode of MEMS device 500 is coupledto a third electrical domain via contacts 509 and 511 of the anchor 504.Portions of the second electrode are suspended from the substrate bybeam 513 extending between the center anchor structure and ends of body502. The hatched regions of MEMS device 500 in FIG. 6C indicate thoseportions of MEMS device 500 that are coupled to the third electricaldomain, other portions of MEMS device 500 (electrically conductive andelectrically insulating) are indicated with dots, and unshaded gaps,e.g., between the electrode teeth and body teeth, may contain air orother fluid. Referring back to FIG. 5, suspension beam 513 includesconductive portions that are defined as part of a third electricaldomain by electrical isolation material 515 embedded in beam 513.However, other portions of beam 513 are electrically isolated from thethird electrical domain by embedded electrical isolation material. Thesecond electrode includes conductive finger structures that areinterdigitated with conductive finger structures of body 502 to form thecomb drive transducers.

Still referring to FIG. 5, MEMS device 500 includes a folded beamstructure. As discussed above, MEMS device 500 includes electricallyinsulating material portions (indicated by hatching in FIG. 5) in thesuspension beams 512 to allow separate signal routing to the body andthe electrodes. Those electrically insulating material portions mayaffect the strain gradient of the suspension beams. If the straingradients between the suspension beams and the body are not matched,those electrically insulating material portions may cause the suspensionbeams to curl differently with respect to the body, resulting in amisalignment of the electrode and body at the transducer gap of the combdrive transducers, thereby reducing transducer efficiency. Referring toFIGS. 5 and 6E, to compensate for changes in strain gradient withrespect to the body due to electrical insulator material in suspensionarms of MEMS device 500, body 502 includes embedded electrical insulatormaterial slits 522. Those electrically insulating material slits havegeometries that match a strain gradient of the body to the straingradient in the suspension beams. As a result of the design features ofMEMS device 500, the static deflection of portions of MEMS device 500including the electrodes is matched to the static deflection of the bodyin the out-of-plane direction, as illustrated by the static deflectionmap of FIG. 6E.

Referring to FIGS. 7A and 7B, MEMS device 700 is an exemplaryhigh-frequency resonator including a suspended mass having multipleanchors but without suspended electrodes. The displacement profile ofFIG. 7A illustrates the target mode shape of the basic shape structure.Each of electrodes 712, 714, 716, and 718 are independently anchored tothe substrate by multiple anchors, which include contacts tocorresponding electrical domains. Plate resonator 702 is separatelyanchored to the substrate by a five-point anchoring technique includingcentral anchor 720 and an anchor 722 at each corner of the plate. Eachcorner anchor includes a decoupling spring 724 and an electricalconnection to a corresponding domain.

FIGS. 8A and 8B illustrate an exemplary high-frequency MEMS device 800including a suspended body and suspended electrodes that aremechanically coupled to each other using electrically insulatingmaterial portions 806. Plate resonator 802 is anchored to the substrateby a central anchor, which also includes an electrical contact to afirst electrical domain. The four corner anchors are mechanicallycoupled to plate resonator 802 using electrically insulating materialportions, but electrically isolated from plate resonator 802 byelectrically insulating material portions. Each of the corner anchorselectrically couples an electrical domain to one of the electrodes(e.g., electrode 816) mechanically coupled to the anchor. Each corneranchor also includes an electrically insulating material portion 808that electrically isolates that electrical domain from another electrodemechanically coupled to the anchor (e.g., electrode 818). Thus, thedesign of MEMS device 800 reduces or eliminates frequency variation dueto strain.

The techniques described above may be applied to other types of MEMSdevices. Electrodes may be suspended above a substrate and mechanicallyreferenced with respect to a suspended resonator beam to reducefrequency variation due to strain. Referring to FIG. 9, a flexuraldevice includes suspended body beam 904 between suspended electrode beam902 and suspended electrode beam 906. Unlike MEMS devices 500, 700, and800, which may be modeled as the system of FIG. 4B having stationaryelectrodes, MEMS device 900 includes a body and electrodes that vibratetogether (i.e., form a vibration mode together). In MEMS device 900,suspended electrodes beams 902 and 906 are tuning-fork-like structuresthat in conjunction with body 904, form a resonator and a transducer atthe same time. Such beam structures may be used in gyroscopes andlow-frequency timing structures. Suspended body beam 904 and suspendedelectrode beams 902 and 906 are electrically isolated and mechanicallycoupled by electrically insulating material portion 908. Any substratestrain causes the electrodes to move together. Thus the electrodes areself-referenced and MEMS device 900 is strain insensitive. Each of thebeams is associated with a different electrical domain, but aremechanically coupled to each other. Electrically insulating materialportion 908 mechanically couples body beam 904 and the suspendedelectrode beams 902 and 906. Routing signal 918 travels throughelectrically insulating material portion 908 and couples body beam 904to anchors 910 and 912, which are mechanically decoupled from body beam904 by decoupling springs 914 and 916 to reduce transfer of strain fromthe substrate to body beam 908 and include electrical contacts to acorresponding electrical domain. Unlike conventional MEMS structures,the electrode beams and body beam of MEMS device 900 vibrate togetherand device 900 has reduced strain sensitivity as compared toconventional MEMS devices since any movement due to strain will causethe electrode beams and body beam to move in a similar manner. Althoughthe mechanical coupling and electrical isolation of electrodes and bodystructures are illustrated for a flexural device, the techniquesdescribed herein may be adapted for bulk acoustic mode devices in whichthe electrically insulating material structure may be designed as partof the mode shape.

Referring back to FIGS. 5 and 6D, in at least one embodiment, MEMSdevice 500 includes multiple temperature compensation structures,portions of which are hatched in FIG. 6D. An individual temperaturecompensation structure includes independent beams having differentstiffness variations as a function of temperature (i.e., differentYoung's modulus temperature coefficients). In at least one embodiment ofthe temperature compensation structure, a first material forming beam508 has a different Young's modulus temperature coefficient than secondmaterial forming beam 506. The Young's modulus temperature coefficientof the first material need only be different than that of the secondmaterial over the operational range of the MEMS device. Any materialhaving a different Young's modulus temperature coefficient than firstmaterial over the typical operating range (e.g., approximately −40° C.to approximately 85° C. or approximately −55° C. to approximately 125°C.) may be employed as second material. In at least one embodiment ofthe temperature compensation structure, the second material has anegative Young's modulus temperature coefficient, while the firstmaterial has a positive Young's modulus temperature coefficient. In atleast one embodiment of the temperature compensation structure, beamspring 508 is formed from the structural material, which may be asemiconductor such as, but not limited to, silicon (Si), germanium (Ge),and SiGe alloys, and beam spring 506 is formed from the electricallyinsulating material, which may be SiO₂ and indicated by hatching inFIGS. 5 and 6D. Note that silicon dioxide has the unusual property ofbecoming stiffer as temperature increases. In other embodiments of thetemperature compensation structure, beam spring 506 is formed from othermaterials, which may have positive or negative Young's modulustemperature coefficients.

The temperature compensation structure may include routing spring 510,which dominates the electrical behavior of the temperature compensationstructure. That is, routing spring 510 is a serpentine structure formedfrom the structural material and routing spring 510 and beam spring 508electrically couple the body to the electrical domain of the centeranchor. Routing spring 510 has a much higher compliance than beam spring506 and beam spring 508. Thus routing spring 510 does not substantiallyinfluence the mechanical behavior but dominates the electrical behaviorof the temperature compensation structure. Beam spring 506 and beamspring 508 have a higher stiffness than routing spring 510 and thusdominate the mechanical behavior of the temperature compensationstructure. Note that the beam springs may be coupled mechanically inseries or in parallel to form a spring that supports the movable bodyand beam springs and routing spring may have other geometries. Thetemperature compensation structure is selectively located to specificregions of MEMS device 500 and beam springs 506 and 508 are dimensionedto modify the temperature response of MEMS device 500 (e.g., thetemperature coefficient of frequency of a resonator) independent ofother properties of the MEMS device (e.g., a resonator mode shape).

This approach can simplify design as compared to other temperaturecompensation techniques that use strips of silicon dioxide surrounded bysilicon germanium on either side or surrounded by strips of silicongermanium. The dual beam technique may also substantially reduce theamount of interface between the two materials. The silicongermanium-silicon dioxide interface can introduce undesirable effectssuch as locally varying properties and the generation of mechanical weakpoints and stress concentrations. Having separate spring portionsfacilitates moving structural weak points and stress concentrationfeatures to less critical locations. The separate beam approach totemperature compensation can reduce thermoelastic energy losses and thusdamping at silicon germanium-silicon dioxide interface, therebyincreasing the quality factor of the resonator, which is a metric forshort-term stability. The separate beam technique may also improvedesign flexibility by allowing independent selection of silicon dioxideand silicon germanium beam dimensions, thereby expanding the designspace available to achieve temperature compensation at any particularfrequency. Unlike temperature compensation techniques that use strips ofoxide surrounded by other material, the dual-beam technique may beeasily adapted to compensate for effects of temperature variations inMEMS devices that use slender flexural beams, e.g., inertial sensors. Inaddition, the dual-beam technique is less sensitive to somemanufacturing tolerances, e.g., pattern alignment of silicon dioxide tosilicon germanium.

Referring to FIGS. 10A and 10B, electrical insulator material embeddedin a MEMS structural layer is used to form suspended resistor 1002 thatis mechanically coupled to a central beam of the resonator. Embeddedelectrical insulator traces 1006 and 1007 electrically isolate andmechanically couple a serpentine portion of structural material tracesto form suspended resistors 1002 and 1003. Suspended resistors 1002 and1003 are mechanically anchored to the substrate by contacts 1008 and1010 and contacts 1012 and 1014, respectively. Contacts 1008 and 1010and contacts 1012 and 1014 serve as the electrical terminals ofsuspended resistors 1002 and 1003, respectively.

Suspended resistors 1002 and/or 1003 may be configured to maintainconstant or otherwise adjust a temperature of MEMS device 1000 byregulating power dissipation into the body 1020. Suspension of theresistor from the substrate improves thermal isolation and using arelatively small thermal mass as compared to heaters that are embeddedin a substrate. The smaller thermal mass is needed to make wafer levelcalibration practical by keeping heating currents low. The suspendedresistor allows on-chip, wafer-level calibration of a resonator with arelatively small thermal mass.

In another embodiment of MEMS device 1000, suspended resistors 1002and/or 1003 are configured to characterize the temperature response ofMEMS device 1000. For example, resistors 1002 and 1003 may be used as atemperature sensor element (i.e., a thermistor) of a bridge temperaturesensor. A change in temperature of body 1020 will cause a correspondingchange in the resistance of resistors 1002 and 1003 by an amountcharacterized by the temperature coefficient of resistance (TCR) of thestructural material (e.g., SiGe). That temperature change can bedetermined based on a voltage drop across the resistor, a predeterminedresistance value at a predetermined temperature, and the TCR of thestructural material. When used as a temperature sensor, the suspendedresistor technique allows placement of the sensing element proximate tothe element (e.g., MEMS resonator 1000) that is having its temperaturesensed and/or compensated. Mechanically coupling the resistor to thecentral beam of the device, via electrically isolating materialportions, reduces effects of strain on the temperature measurement. Suchplacement reduces thermal gradients and associated temperaturemeasurement errors, which results in a sensor that is more accurate overtemperature than other sensors and measures temperature where itmatters, i.e., at the location of the device that needs compensation fortemperature shifts.

MEMS device 1000 is an exemplary lattice transducer that may beconfigured to generate a target frequency using a torsional mode or aflexural mode. MEMS device 1000 includes body 1020 formed from latticebeams that are suspended from the substrate. Body 1020 is anchored tothe substrate by anchors 1016 and 1018, which are coupled to body 1020by decoupling springs. Anchors 1016 and 1018 also provide electricalcontact to the body 1020. The lattice beams of body 1020 formsubstantially square lattice openings that surround, but do not touch,corresponding electrodes that are anchored to the substrate. Eachsubstantially square lattice opening forms a transducer gap along theperimeter of the opening and the perimeter of the substantially squareelectrode 1022. Note that the perimeter of the lattice openings and theperimeter of the electrodes have a varied perimeter that increases thearea of the transducers. However, the perimeters of the lattice openingsand the electrodes may have other geometries. MEMS device 1000, asillustrated, includes eighteen transducers on each side of the centeranchors 1016 and 1018, however, the number of transducers is exemplaryonly and may vary according to application.

Although the suspended passive element technique is illustrated in anembodiment including a lattice transducer, the suspended passive elementtechnique may be incorporated into MEMS devices having any type oftransducers and/or having mechanically coupled electrodes and body(e.g., MEMS device 500). For example, FIG. 10C illustrates the suspendedpassive resistor in an embodiment including beams 1038 and 1040 andlateral electrodes 1030, 1032, 1034, and 1036. In addition, althoughtechniques described above illustrate the use of insulator materialembedded in a MEMS structural layer to form electrostatic transducersand suspended resistors, the technique may be used for other types ofpassive elements, which may be used in filters, switches, or otherapplications. For example, by using a structural material that has a lowresistivity, the technique may be used to form suspended inductors(e.g., planar spiral inductors) that have a high quality factor (i.e.,low eddy currents) or to form electromechanical switches that are strainfree for improved manufacturability, lower switching voltages, andimproved reliability (e.g., reduced risk of stiction).

The description of the invention set forth herein is illustrative, andis not intended to limit the scope of the invention as set forth in thefollowing claims. For example, while the invention has been described inembodiments in which specific MEMS structures (e.g., comb drive,parallel plate, and lattice transducers) and materials (e.g., SiGe andSiO₂) are used, one of skill in the art will appreciate that theteachings herein can be utilized with other types of MEMS structures andmaterials. Variations and modifications of the embodiments disclosedherein, may be made based on the description set forth herein, withoutdeparting from the scope and spirit of the invention as set forth in thefollowing claims.

What is claimed is:
 1. An apparatus comprising: a microelectromechanicalsystem (MEMS) device comprising: a first electrode and a secondelectrode; and a body suspended from a substrate, the body and the firstelectrode forming a first electrostatic transducer, and the body and thesecond electrode forming a second electrostatic transducer, wherein thebody comprises: a temperature compensating structure comprising: a firstbeam suspended from the substrate, the first beam being formed from afirst material having a first Young's modulus temperature coefficient;and a second beam suspended from the substrate, the second beam beingformed from a second material having a second Young's modulustemperature coefficient.
 2. The apparatus, as recited in claim 1,wherein the second material has a higher electrical conductivity thanthe first material.
 3. The apparatus, as recited in claim 1, wherein thefirst beam and the second beam are mechanically coupled in series. 4.The apparatus, as recited in claim 1, wherein the body furthercomprises: a routing spring suspended from the substrate, the routingspring coupled to the first beam and the second beam, the routing springbeing formed from the second material.
 5. The apparatus, as recited inclaim 4, wherein the routing spring has a serpentine structure.
 6. Theapparatus, as recited in claim 4, wherein the electrical conductivity ofthe routing spring dominates electrical conductivity of the temperaturecompensating structure.
 7. The apparatus, as recited in claim 4, whereinthe first beam and the second beam have lower spring compliance than therouting spring.
 8. The apparatus, as recited in claim 4, wherein themechanical behavior of the first beam and the second beam dominates themechanical behavior of the temperature compensating structure.
 9. Theapparatus, as recited in claim 1, wherein the first Young's modulustemperature coefficient is positive and the second Young's modulustemperature coefficient is negative.
 10. The apparatus, as recited inclaim 1, wherein the MEMS device is a resonator and the temperaturecompensating structure has dimensions and a location such that thetemperature compensation structure modifies a temperature coefficient offrequency of the resonator independent of a mode shape of the resonator.11. A method of manufacturing an apparatus comprising: forming amicroelectromechanical system (MEMS) device comprising: a firstelectrode and a second electrode; and a body suspended from a substrate,the body and the first electrode forming a first electrostatictransducer, and the body and the second electrode forming a secondelectrostatic transducer, wherein the body comprises: a temperaturecompensating structure comprising: a first beam suspended from thesubstrate, the first beam being formed from a first material having afirst Young's modulus temperature coefficient; and a second beamsuspended from the substrate, the second beam being formed from a secondmaterial having a second Young's modulus temperature coefficient. 12.The method, as recited in claim 11, wherein the second material has ahigher electrical conductivity than the first material.
 13. The method,as recited in claim 11, wherein the first beam and the second beam aremechanically coupled in series.
 14. The method, as recited in claim 11,wherein the MEMS device further comprises a routing spring suspendedfrom the substrate, the routing spring coupled to the first beam and thesecond beam, the routing spring being formed from the second material.15. The method, as recited in claim 14, wherein the routing spring has aserpentine structure.
 16. The method, as recited in claim 14, whereinthe electrical conductivity of the routing spring dominates electricalconductivity of the temperature compensating structure.
 17. The method,as recited in claim 14, wherein the first beam and the second beam havelower spring compliances than the routing spring.
 18. The method, asrecited in claim 14, wherein the mechanical behavior of the first beamand the second beam dominates the mechanical behavior of the temperaturecompensating structure.
 19. The method, as recited in claim 11, whereinthe first Young's modulus temperature coefficient is positive and thesecond Young's modulus temperature coefficient is negative.
 20. Anapparatus comprising: means for vibrating, wherein the means forvibrating is suspended from a substrate; means for electrostaticallydriving the means for vibrating; means for electrostatically sensingvibrations of the means for vibrating; and means for compensating forvariations in frequency of vibrations due to a change in temperatureusing a first suspended structure formed from a first material having afirst Young's modulus temperature coefficient and a second suspendedstructure formed from a first material having a first Young's modulustemperature coefficient.